Entropy production and phase transitions far from equilibrium with emphasis on wet granular matter

This thesis investigates irreversible dynamics. It is shown analytically that the recent Fluctuation Theorem extends to relativistic dynamics. In the analytic consideration of non-relativistic granular gases with broken time-reversal symmetry we find violations of the Fluctuation Theorem for large fluctuations. This is confirmed by simulations of wet granular matter in driven stationary states. It is shown that the theorem persists to hold for small fluctuations, which explains earlier reports of confirmation in literature as a consequence of their measurement range. The particle interaction in wet granular matter is experimentally shown to be hysteretic with the formation and rupture of capillary bridges. The measured dissipation is quantified by the rupture length and energy of the bridges. For a kinematic description of wet granular matter based on these experimental findings, the Enskog factor is generalized analytically to a set of six fa tors, which acount for the hysteretic interaction in a statistical description. Such a statistical and, moreover, continuum description is made possible by the analytical and numerical computations of the Kolmogorov-Sinai entropy, which demonstrates the substantial increase of dynamical chaos due to the capillary interaction in wet granular matter. On this basis, the equation of state of wet granular matter is derived analytically. A van-der-Waals-like mechanical instability is predicted, and verified in simulations and experiments. In the simulations, the instability leads to the breakup of capillary bridges. This nonequilibrium dynamics is described analytically by a mean-field theory in quantitative agreement with the simulations. The experimentally determined critical point of this instability agrees quantitatively with the theory. A novel method, which allows to measure the velocity distribution in nonequilibrium steady states of granular matter based on the Mössbauer effect, is suggested. In a first measurement, an exponential velocity distribution is observed for the fluid-like state. It is demonstrated that the global instantaneous state of the dynamical capillary network in wet granular matter is observable by electrical conductivity, when an ionic liquid is added. This allows to detect the transition of wet granular matter from the solid to the fluid state in the bulk, excluding surface effects, and to demonstrate experimentally with unprecedented precision that this transition is discontinuous and hysteretic with respect to the external driving. Simulations and experiments show that this nonequilibrium transition sets in at a critical acceleration of the external driving. Furthermore, the transition from the fluid-like to the gaseous state of wet granular matter is demonstrated experimentally and by simulations. In both approaches it is shown quantitatively that this transition is determined by a critical velocity of the driving, which is directly related to the capillary energy. States of fluid/gas coexistence, which emerge in experiments and simulations are explained analytically as subcritical instabilities in the balance of power. Applying the derived equation of state, the spatial distributions of temperature, density and dissipation are computed. Order parameters are measured, and the global phase diagram of the nonequilibrium states and transitions of wet granular matter is presented